Determine the coordinates of the endpoint of a segment CE with one endpoint at C(3,10) and a midpoint at (-1,-6).

Disclaimer: This is 10th grade geometry.

The midpoint is halfway from one end to the other. Just figure out ho wfar you've gone and go twice that far.

(-1,-6) - (3,10) = (-4,-16)

That is, you've added (-4,-16) to (3,10) to get to (-1,-6).

So, add it again:

(-1,-6) + (-4,-16) = (-5,-22)

Let the endpoint be (x,y)

so ..
(x+3)/2 = -1 and (y+10)/2 = -6
x+3 = -2 and y+10 = -12
x = -5 and y = -22
endpoint is (-5,-22)

To determine the coordinates of the endpoint of segment CE, we can use the midpoint formula, which states that the coordinates of the midpoint of a line segment are the average of the coordinates of its endpoints.

Let's denote the coordinates of the endpoint of segment CE as (x,y).

Given that the midpoint of segment CE is (-1,-6) and one endpoint is C(3,10), we can use the midpoint formula:

Midpoint(x-coordinate) = (x1 + x2) / 2
Midpoint(y-coordinate) = (y1 + y2) / 2

Substituting the known values into the formula, we have:

-1 = (3 + x) / 2
-6 = (10 + y) / 2

To solve these equations, we can isolate x in the first equation and y in the second equation.

Multiply both sides of the first equation by 2:
-2 = 3 + x

Subtract 3 from both sides:
-2 - 3 = x
-5 = x

Multiply both sides of the second equation by 2:
-12 = 10 + y

Subtract 10 from both sides:
-12 - 10 = y
-22 = y

Therefore, the coordinates of the endpoint of segment CE are (-5, -22).